Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x-y+3z = 12
x+4y+6z =-32
5x+3y+9z = 20
Enter your coefficients here and see all the details:
http://www.gregthatcher.com/Mathematics/GaussJordan.aspx
I don't know how to use that
When I do it , it says Im wrong
well, when I do it, it says I'm right, so why don't you show your work here and we can see how things go?
How did you do it ? what do you put in the boxes ?
I actually have to show my work , But I need help with this
I'll get you started. But you clearly need to study the examples in your text. Or, just do a google and you will find lots of examples online.
You start with your matrix of coefficients:
4 -1 3 | 12
1 4 6 | -32
5 3 9 | 20
You want to work things so that you have a final matrix with the left side looking like
1 0 0
0 1 0
0 0 1
And then the 4th column will have the values of the variables.
So, starting with
4 -1 3 | 12
1 4 6 | -32
5 3 9 | 20
if you multiply the 2nd row by 4 you have
4 -1 3 | 12
4 16 24 | -128
5 3 9 | 20
Now if you subtract the top row from the 2nd row, you have
4 -1 3 | 12
0 17 21 | -140
5 3 9 | 20
Now multiply the 3rd row by 4 and you have
4 -1 3 | 12
0 17 21 | -140
20 12 36 | 80
Now subtract the top row from the 3rd row and you have
4 -1 3 | 12
0 17 21 | -140
0 17 21 | 20
Woah! At this point you have
17y+21z = -140
17y+21z = 20
so there is no solution, since -140 ≠ 20
You really should go back to the web site and play around with some numbers just to get used to how it works.